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R E Volker - One of the best experts on this subject based on the ideXlab platform.

  • numerical correction for Finite Difference Solution of the advection dispersion equation with reaction
    Journal of Contaminant Hydrology, 1996
    Co-Authors: Behzad Ataieashtiani, D A Lockington, R E Volker
    Abstract:

    Abstract A correction for truncation errors associated with a Finite-Difference Solution of the advection-dispersion equation with reaction is developed from a Taylor analysis. An explicit Finite-Difference scheme is used to show the effect of these truncation errors on the Solution of an advection-dispersion equation with a first-order reaction term. The criteria for the stability of the Finite-Difference Solutions are derived using a matrix method proposed by Smith (1978). Comparison with an analytical Solution shows that the uncorrected errors are not negligible and that by correcting the Finite-Difference scheme for them the results will be more accurate. The approach can also be used for correcting other Finite-Difference schemes whenever they do not have second-order accuracy.

Behzad Ataieashtiani - One of the best experts on this subject based on the ideXlab platform.

  • numerical correction for Finite Difference Solution of the advection dispersion equation with reaction
    Journal of Contaminant Hydrology, 1996
    Co-Authors: Behzad Ataieashtiani, D A Lockington, R E Volker
    Abstract:

    Abstract A correction for truncation errors associated with a Finite-Difference Solution of the advection-dispersion equation with reaction is developed from a Taylor analysis. An explicit Finite-Difference scheme is used to show the effect of these truncation errors on the Solution of an advection-dispersion equation with a first-order reaction term. The criteria for the stability of the Finite-Difference Solutions are derived using a matrix method proposed by Smith (1978). Comparison with an analytical Solution shows that the uncorrected errors are not negligible and that by correcting the Finite-Difference scheme for them the results will be more accurate. The approach can also be used for correcting other Finite-Difference schemes whenever they do not have second-order accuracy.

Khalil Khanafer - One of the best experts on this subject based on the ideXlab platform.

  • non darcy natural convection heat and mass transfer along a vertical permeable cylinder embedded in a porous medium
    International Journal of Thermal Sciences, 1999
    Co-Authors: M A Hossain, Kambiz Vafai, Khalil Khanafer
    Abstract:

    Abstract Combined heat and mass transfer in non-Darcy natural convection flow along a permeable vertical cylinder embedded in a saturated porous medium is studied. The boundary layer analysis is formulated in terms of the combined thermal and solutal buoyancy effect. The flow field characteristics are analyzed using the implicit Finite Difference method as well as the local nonsimilarity method. The effect of the curvature, the buoyancy ratio, the Lewis number and the transpiration parameter on the local Nusselt number and the local Sherwood number are also studied. The results are presented in tabular form as well as graphically. Comparisons of the results obtained by the local nonsimilarity method are in excellent agreement with Finite Difference Solution up to χ (the curvature parameter) of 10. The effects of different pertinent parameters on the velocity, temperature and species concentration profiles are also shown graphically.

Jumat Sulaiman - One of the best experts on this subject based on the ideXlab platform.

  • On redlich-kister Finite Difference Solution of two-point boundary value problems using half-sweep kaudd successive over relaxation iteration
    'Seventh Sense Research Group Journals', 2021
    Co-Authors: Mohd Norfadli Suardi, Jumat Sulaiman
    Abstract:

    This paper deals with the application of two newly established Redlich-Kister Finite Difference (RKFD) discretization schemes for approximating and solving two-point boundary value problems (TPBVPs). To get the Redlich-Kister Finite Difference Solution of the proposed problem, firstly, two newly second-order half-sweep RKFD discretization schemes are established and used to discretize overall derivative terms of the TPBVPs regarding getting the second-order half-sweep RKFD approximation equation. Then this RKFD approximation equation leads to the construct of the linear system. Due to the increase in the convergence rate iteratively in solving this linear system, the combination of the Kaudd Successive Over Relaxation (KSOR) method with a half-sweep approach is formulated and then known as Half-sweep Kaudd Successive Over Relaxation (HSKSOR) method. With the purpose of evaluating the efficiency of the HSKSOR method, other methods such as Full-sweep Kaudd Successive Over Relaxation (FSKSOR) and Full-sweep Gauss-Seidel (FSGS) are also presented as a control method. The results of the examples of TPBVPs are tested to prove that the HSKSOR iteration is more efficient compared with FSGS and FSKSOR iterations in terms of iterations, execution time, and maximum norm

  • Rational Finite Difference Solution of first-order fredholm integro-differential equations via SOR iteration
    2021
    Co-Authors: Jumat Sulaiman, Labiyana Hanif Ali
    Abstract:

    The linear rational Finite Difference method (LRFD) is becomingmore and more popular recently due to its excellent stability properties and convergence rate, especially when we are approximating the derivative of some points near the end of the interval. The main intention of this paper is to combine the 3-point linear rational Finite Difference (3LRFD) method with the composite trapezoidal (CT) quadrature formula to discretize the first-order linear integro-differential equation and produce dense linear systems. Furthermore, the numerical Solution of the integrodifferential equation is obtained by implementing the Successive Over-Relaxation (SOR) method. At the same time, the classical Gauss–Seidel (GS) method is also introduced as the control condition. In the end, through several numerical examples, the number of iterations, the execution time and the maximum absolute error are compared, which fully illustrated the superiority of SOR method over GS method in solving large dense linear system generated by the CT-3LRFD formula

  • Redlich-Kister Finite Difference Solution for solving two-point boundary value problems by using KSOR iteration family
    'ASTES Journal', 2021
    Co-Authors: Mohd Norfadli Suardi, Jumat Sulaiman
    Abstract:

    In this paper, we are concerned to investigate the efficiency of the second-order RedlichKister Finite Difference (RKFD) discretization scheme together with the Four Point Explicit Group Kaudd Successive Over Relaxation (4EGKSOR) iterative method for solving two-point boundary value problems (TPBVPs). In order to apply this block iteration to solve any linear system, firstly we discretize all derivative terms via the second-order RKFD discretization scheme over the proposed problem in order to get the second-order RKFD approximation equation. Due to the main characteristics of the coefficient matrix for the generated linear system which are large-scale and sparse, the best choice for solving this linear system is using one of the iterative methods. Therefore, the formulation of the Kaudd Successive Over Relaxation method together with the Explicit Group iteration method mainly on the Four-Point Explicit Group Kaudd Successive Over Relaxation (4EGKSOR) iterative method has been presented to solve this linear system iteratively. In order to show the efficiency of the 4EGKSOR, another two iterative methods have also been considered which are the Gauss-Seidel (GS) and the Kaudd Successive Over Relaxation (KSOR) to solve three examples of the proposed problems in which all numerical results obtained were recorded based on the number of iterations, execution time and maximum norm. Based on the performance analysis, clearly, the 4EGKSOR iterative method shows substantiated improvement in terms of the number of iterations and execution time

  • implicit Finite Difference Solution for time fractional diffusion equations using aor method
    Journal of Physics: Conference Series, 2014
    Co-Authors: Andang Sunarto, Jumat Sulaiman, Azali Saudi
    Abstract:

    In this paper, we derive an implicit Finite Difference approximation equation of the one-dimensional linear time fractional diffusion equations, based on the Caputo's time fractional derivative. Then this approximation equation leads the corresponding system of linear equation, which is large scale and sparse. Due to the characteristics of the coefficient matrix, we use the Accelerated Over-Relaxation (AOR) iterative method for solving the generated linear system. One example of the problem is presented to illustrate the effectiveness of AOR method. The numerical results of this study show that the proposed iterative method is superior compared with the existing one weighted parameter iterative method.

Christopher J. Bean - One of the best experts on this subject based on the ideXlab platform.

  • A 3D discrete numerical elastic lattice method for seismic wave propagation in heterogeneous media with topography
    Geophysical Research Letters, 2004
    Co-Authors: Gareth S. O'brien, Christopher J. Bean
    Abstract:

    [1] A three-dimensional elastic lattice method for the simulation of seismic waves is presented. The model consists of particles arranged on a cubic lattice which interact through a central force term and a bond-bending force. Particle disturbances are followed through space by numerically solving their equations of motion. A vacuum free-surface boundary condition is implicit in the method. We demonstrate that a numerical implementation of the method is capable of modelling seismic wave propagation with complex topography. This is achieved by comparing the scheme against a Finite-Difference Solution to the elastodynamic wave equation. The results indicate that the scheme offers an alternative 3D method for modelling wave propagation in the presence of strong topography and subsurface heterogeneity. We apply the method to seismic wave propagation on Mount Etna to illustrate its applicability in modelling a physical system.

  • numerical simulation of seismic waves using a discrete particle scheme
    Geophysical Journal International, 2000
    Co-Authors: Aoife Toomey, Christopher J. Bean
    Abstract:

    Summary A particle-based model for the simulation of wave propagation is presented. The model is based on solid-state physics principles and considers a piece of rock to be a Hookean material composed of discrete particles representing fundamental intact rock units. These particles interact at their contact points and experience reversible elastic forces proportional to their displacement from equilibrium. Particles are followed through space by numerically solving their equations of motion. We demonstrate that a numerical implementation of this scheme is capable of modelling the propagation of elastic waves through heterogeneous isotropic media. The results obtained are compared with a high-order Finite Difference Solution to the wave equation. The method is found to be accurate, and thus offers an alternative to traditional continuum-based wave simulators.